Yahoo Answers: Answers and Comments for Find the max area or rectangle [數學]
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From Lau
zhHantHK
Sun, 02 Jan 2011 16:55:32 +0000
3
Yahoo Answers: Answers and Comments for Find the max area or rectangle [數學]
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https://hk.answers.yahoo.com/question/index?qid=20110102000051KK00902
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From myisland8132: The key point is to find out the relation betw...
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https://hk.answers.yahoo.com/question/index?qid=20110102000051KK00902
Sun, 02 Jan 2011 17:22:55 +0000
The key point is to find out the relation between x and y.
Since triangle ADE is similar to the triangle DCF
DE/CF=AE/CF
x/(8x)=(4y)/y
xy=(8x)(4y)
xy=324x8y+xy
4x+8y=32
x+2y=8
x=82y
Now the Area of the rectangle is xy
=y(82y)
=2y^2+8y
=(y4)^2+16
which attains the maximum value 16 when y=4. So, the maximum area of the rectangle is 16 cm^2.
20110102 17:24:33 補充：
Some mistakes Sorry
=y(82y)
=2y^2+8y
=2(y4)^2+8
which attains the maximum value 8 when y=4. So, the maximum area of the rectangle is 8 cm^2.

From 螞蟻雄兵: Sol
(4－x)：4=y：8
4y=8(4－x)
y=2(4－x)
y=8－2x
xy...
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https://hk.answers.yahoo.com/question/index?qid=20110102000051KK00902
Sun, 02 Jan 2011 17:14:34 +0000
Sol
(4－x)：4=y：8
4y=8(4－x)
y=2(4－x)
y=8－2x
xy=x(8－2x)
=－2x^2+8x
=－2(x^2－4x)
=－2(x^2－4x+4)+8
=－2(x－2)^2+8
0<4
－2<2
0<=(x－2)^2<4
－4<－(x－2)^2<=0
－8<=－2(x－2)^2<=0
0<－2(x－2)^2+8<=8
０<=8
max=8

From 蛙人: Using similar triangle,
y/8 = (4x)/4
y = 8  ...
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https://hk.answers.yahoo.com/question/index?qid=20110102000051KK00902
Sun, 02 Jan 2011 17:07:15 +0000
Using similar triangle,
y/8 = (4x)/4
y = 8  2x
So area of rectangle = xy
= x(8  2x)
= 2(x^2  4x)
= 2(x^2  4x + 4  4)
= 2(x  2)^2 + 8
Thus the maximum area is 8cm^2